Square Root Of 46656 In Simplest Radical Form
Simplify the square root of 46656 to its lowest radical form.ANSWER: 216√1
216√1 is in the lowest radical form.
Simplified Radical Form of √46656
One of the main facts used to simplify square roots is that the square root of a product is equal to the product of square roots: √(x×y) = √x×√y
Explanation:
When we find square root of any number, we take one number from each pair of the same numbers from its prime factorization and we multiply them.
Step 1: List Factors
To simplify √46656, we need to divide into factors.
√46656 = √2 x √2 x √2 x √2 x √2 x √2 x √3 x √3 x √3 x √3 x √3 x √3Step 2: List Perfect Squares
1 is a perfect square and divides 46656
4 is a perfect square and divides 46656
9 is a perfect square and divides 46656
16 is a perfect square and divides 46656
36 is a perfect square and divides 46656
64 is a perfect square and divides 46656
81 is a perfect square and divides 46656
144 is a perfect square and divides 46656
324 is a perfect square and divides 46656
576 is a perfect square and divides 46656
729 is a perfect square and divides 46656
1296 is a perfect square and divides 46656
2916 is a perfect square and divides 46656
5184 is a perfect square and divides 46656
11664 is a perfect square and divides 46656
46656 is a perfect square and divides 46656
Step 3: Divide To Perfect Square
Divide 46656 by the largest perfect square you found in the previous step:
Step 4: Calculate The Square Root
Calculate the square root of the largest perfect square:
Final Step :
Put Steps 3 and 4 together to get the square root of 46656 in its simplest form: 216√1
How do you simplify √46656
The general approach is to first check if it is a perfect square. If so, you have the answer. If it is not a perfect square, see if any of its factors are perfect squares, or can be combined to make square numbers.
Find the lowest prime number that can divide 46656. Divide 46656 repeatedly using the long division method till you reach 1.
A pair of factor 'twins' under a square root sign (radical) form a single factor outside of it.
Factors that do not have a twin remain under the radical. Multiply them back together and leave them in there.
So, the answer is 216√1.
Simplified Decimal Form of √46656
The square root of 46656 is approximately 216 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √86 | Square root of 86 is the simplest radical form. | √2 x √43 |
| √18 | 3√2 | √2 x √3 x √3 |
| √61 | Square root of 61 is the simplest radical form. | √61 |
| √705 | Square root of 705 is the simplest radical form. | √3 x √5 x √47 |
| √554 | Square root of 554 is the simplest radical form. | √2 x √277 |
| √152 | 2√38 | √2 x √2 x √2 x √19 |
| √1893 | Square root of 1893 is the simplest radical form. | √3 x √631 |
| √4211 | Square root of 4211 is the simplest radical form. | √4211 |
| √7311 | Square root of 7311 is the simplest radical form. | √3 x √2437 |